The rockwell hardness of a metal is determined byimpressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. suppose the rockwell hardness of a particular alloy is normally distributed with mean 70 and standard deviation 3. (rockwell hardness is measured on a continuous ) if a specimen is acceptable only if its hardness is between 67 and 75, what is the probability that a randomly chosen specimen has an acceptable hardness? (b) if the acceptable range of hardness is (70-c, 70+c) for what value of c would 95% of all specimens haveacceptable hardness? (c) if the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten? (d) what is the probability that at most eight of ten independently selected specimens have a hardness of less than73.84? [hint: y = the number among the ten specimens with hardness less than 73.84 is a binomial variable; what is p?

Study the following reaction carefully. what classification should this reaction have? 4al + 3o2 2al2o3synthesisdecompositionsingle replacementdouble displacement

On a horizontal frictionless surface, a small block with mass 0.200 kg has a collision with a block of mass 0.400 kg. immediately after the collision, the 0.200 kg block is moving at 12.0 m/s in the direction 30° north of east and the 0.400 kg block is moving at 11.2 m/s in the direction 53.1° south of east. use coordinates where the +x-axis is east and the +y-axis is north.(a) what is the total kinetic energy of the two blocks after the collision (in ) what is the x-component of the total momentum of the two blocks after the collision? (indicate the direction with the sign of your ) what is the y-component of the total momentum of the two blocks after the collision? (indicate the direction with the sign of your answer.)

The inside surface of a cylindrical-shaped cave of inner diameter 1.0 m is continuously covered with a very thin layer of water. the cave is very long and it is open on both ends. the water on the cave surface is at a constant temperature of 15.5 °c. the cave is constantly exposed to wind such that 15.5 °c air flows through the cave at 4.5 m/s. the kinematic viscosity of the air is 14.66 x 10-6 m2/s and the molecular diffusion coefficient of water vapor in the air is 0.239 x 10-4 m2/s. because the cave diameter is so large, the flow of wind down the length of the cave, in the x direction, can be treated like it is external flow and the cave surface can be approximated as flat where appropriate. calculate the x value, in a) the transition to turbulent flow occurs at rex meters, where the air flow transitions from laminar to turbulent along the inside surface of the cave b) calculate the x value, in meters, where the bulk steady state concentration of water vapor in the air flowing in the cave is 10% of the saturation concentration. assume the air at the surface of the water layer is 100% saturated with water vapor. assume the wind entering the cave contained no moisture before it entered the cave. take into account the transition from laminar to turbulent flow when solving part b